The use of low bit-rate audio encoding requires filtering in the decoding post-processing, which can occur in various forms:                customizing the listening experience by changing the characteristic sound of the recording, in particular by attenuating or amplifying certain bands of the audio spectrum,        applying filtering in the audio encoding as well, where configuration tools allow enhancing the audio signal received.        
For example, techniques such as Spectral Band Replication (SBR) or Parametric Stereo (PS) (ISO/IEC 14496-3 standard, MPEG-4 Audio standard) respectively allow reconstructing higher frequency sounds from lower frequencies and stereo sound from a mono signal. MPEG Surround MPS (ISO/IEC 23003-1 standard, MPEG-D standard) extends the approach of PS processing to the reconstruction of more than two audio channels.
In these techniques, the missing portions of the sound are reconstructed by signal copying and filtering operations.
For example, SBR processing modulates the lower frequency areas to higher frequencies and adjusts the frequency energy of the signal. This adjustment allows obtaining a signal after decoding that is similar to the original signal (signal before encoding).
PS processing recreates, from a mono signal, two composite signals in which the frequency energy is adjusted, again in order to render a decoded signal resembling the original reference signal. MPS processing extends this principle to the generation of N signals from M transmitted audio channels (where N≧M).
Low bit-rate audio encoders using transforms according to MPEG standards such as MP3, AAC or USAC, or according to ITU-T standards such as G.722.1, G.719, G.718, prefer the use of critically sampled transforms. Critical sampling is an important property in low bit-rate encoding. In effect, in order to maintain transmission efficiency, there should not be more transformed samples transmitted than there were in the time domain.
For this reason, in current low bit-rate encoders, only critically sampled transforms are employed. These are, for example, MDCT (Modified Discrete Cosine Transform) transforms which are typically transforms with real number coefficients.
These transforms are unsuitable for filtering without artifacts, because they result in a distortion known as “aliasing”.
To achieve adequate filtering, two families of techniques can be applied:                1. those consisting of performing the inverse transformation, then applying a convolution-type filtering;        2. those consisting of using a transformation adapted for filtering (for example a short-term Fourier transform or another transformation for complex values, for example complex filters such as PQMF for Pseudo Quadrature Mirror Filters), which is not critically sampled, in order to be able to perform this filtering operation without artifacts: the filtering then consists of a simple multiplication by transform coefficient (equalization). However, the inverse transformation of the encoding transformation must be performed, then the samples must be transposed to the domain of complex values; after equalization, the samples are restored by inverse complex transformation in the time domain. Three transformations are therefore necessary.        
To carry out the first approach (point 1 above), a convolution-type filtering must be performed after inverse transformation of the encoding, which is costly in terms of computation and is not very versatile (little flexibility in making changes to the implemented filter).
The second approach (point 2) is much more versatile, and it is easy to change the multiplier coefficients (the equalization function). On the other hand, the number of transformations to be applied leads to significant complexity.